Spring 2024 Geometric Topology (MAS630) (Preliminary Syllabus)


Time: Tuesday, Thursday 1:00-2:15
Lecture room: E2-1225
Instructor: Suhyoung Choi E6-1-4403(office)

Office Hours: TBA
email: schoixk at kaist dot ac dot kr
Phone: 2732

The purpose of the course is to learn geometric structures on orbifolds for the first 6 weeks. These are standard materials. From the 7th week, we will cover convex real projective orbifold with ends. I will give the summary lectures of the book chapters in class to be recorded by Zoom and to be uploaded to YouTube. We will be give you the materials at least before two weeks in the KLMS. The second part of the course is very much experimental and you will be required to help with the writing, which will be the assignments. .

Course book: 
Geometric structures on 2-orbifolds: exploration of discrete symmetry MSJ Memoirs, Vol. 27. 171pp + xii, Download at Project Euclid
``Real projective orbifolds with ends and their deformation spaces: the deformation theory for the nice ones,'' We plan revise this many times during Spring of 2024.

Helpful books: 
Foundations of Hyperbolic Manifolds, J. Ratcliffe, Springer, Download from the library
Three-Dimensional Geometry and Topology, Vol. 1, by William P. Thurston (Author), Silvio Levy (Editor), Princeton University Press
Orbifolds and Stringy Topology by Adem, Leida, and Ruan, Cambridge University Press


Grading:

There will be 5-6 homework assignments. Some of these will be problem making ones. These will be reports to be uploaded to KLMS. For the second part, you will be asked to help me revise the book. This course will have really no concrete grading based on points. The participation score will be important.

There is no midterm or final exams.



Schedule: (tentative)
2.26 week: Chapter 2. Manifolds and G-structures
3.4 week: Chapter 3. Geometry and discrete groups
3.11 week: Chapter 4. Topology of orbifolds
3.18 week: Chapter 4. Topology of orbifolds
3.25 week: Chapter 5. Topology of 2-orbifolds, Chapter 6. Geometry of orbifolds
4.1 week: Chapter 7. Deformation spaces of hyperbolic structures on 2-orbifolds
4.8 week: Introduction to convex real projective orbifolds with ends  
4.15 week: The midterm exam period
4.22 week: Preliminary, Example, Introduction to convex radial ends (Chapters 1,2)
4.29 week: Affine actions and totally geodesic ends (Chapters 3, 4, 5)
5.6 week: Radial ends (Chapters 5, 6, 7). We begin Chapter 7 here.
5.13 week: NPNC-ends (Chapters 7)
5.20 week: Complete ends, Openness of deformations (Chapters 8, 9)
5.27 week: Relative hyperbolicity (Chapter 10), Openness and closedness (Chapter 11)

6.3. week: Nicest cases, Appendix (Chapter 12, Appendix) (June 6th holiday)
6.10. week: The final exam period